1 #define IOS ios_base::sync_with_stdio(0); cin.tie(0);
2 #include <cstdio>//sprintf islower isupper
3 #include <cstdlib>//malloc exit strcat itoa system("cls")
4 #include <iostream>//pair
5 #include <fstream>//freopen("C:\\Users\\13606\\Desktop\\Input.txt","r",stdin);
6 #include <bitset>
7 //#include <map>
8 //#include<unordered_map>
9 #include <vector>
10 #include <stack>
11 #include <set>
12 #include <string.h>//strstr substr strcat
13 #include <string>
14 #include <time.h>// srand(((unsigned)time(NULL))); Seed n=rand()%10 - 0~9;
15 #include <cmath>
16 #include <deque>
17 #include <queue>//priority_queue<int, vector<int>, greater<int> > q;//less
18 #include <vector>//emplace_back
19 //#include <math.h>
20 #include <cassert>
21 #include <iomanip>
22 //#include <windows.h>//reverse(a,a+len);// ~ ! ~ ! floor
23 #include <algorithm>//sort + unique : sz=unique(b+1,b+n+1)-(b+1);+nth_element(first, nth, last, compare)
24 using namespace std;//next_permutation(a+1,a+1+n);//prev_permutation
25 //******************
26 clock_t __START,__END;
27 double __TOTALTIME;
28 void _MS(){__START=clock();}
29 void _ME(){__END=clock();__TOTALTIME=(double)(__END-__START)/CLOCKS_PER_SEC;cout<<"Time: "<<__TOTALTIME<<" s"<<endl;}
30 //***********************
31 #define rint register int
32 #define fo(a,b,c) for(rint a=b;a<=c;++a)
33 #define fr(a,b,c) for(rint a=b;a>=c;--a)
34 #define mem(a,b) memset(a,b,sizeof(a))
35 #define pr printf
36 #define sc scanf
37 #define ls rt<<1
38 #define rs rt<<1|1
39 typedef pair<int,int> PII;
40 typedef vector<int> VI;
41 typedef unsigned long long ull;
42 typedef long long ll;
43 typedef double db;
44 const double E=2.718281828;
45 const double PI=acos(-1.0);
46 const ll INF=(1LL<<60);
47 const int inf=(1<<30);
48 const double ESP=1e-9;
49 const int mod=(int)1e9+7;
50 const int N=(int)1e6+10;
51
52 int n,L;
53 int a[N];
54 db dp[N],sum[N];
55 db A(int x)
56 {
57 return sum[x]+x;
58 }
59 db B(int x)
60 {
61 return sum[x]+x+L+1;
62 }
63 db X(int x)
64 {
65 return B(x);
66 }
67 db Y(int x)
68 {
69 return dp[x]+B(x)*B(x);
70 }
71 double slope(int a,int b)
72 {
73 return 1.0*(Y(a)-Y(b))/(1.0*(X(a)-X(b)));
74 }
75
76 class mydeque{
77 public:
78 int len=1000000;
79 int p[N];
80 int l,r,tot;
81 void init()
82 {
83 l=1;r=1;
84 tot=1;
85 }
86 int size()
87 {
88 return tot;
89 }
90 int pos(int x)
91 {
92 return (x+len)%len;
93 }
94 int f()
95 {
96 return p[l];
97 }
98 int b()
99 {
100 return p[r];
101 }
102 void pf(int x)
103 {
104 tot++;
105 l=pos(l-1);
106 p[l]=x;
107 }
108 void pb(int x)
109 {
110 tot++;
111 r=pos(r+1);
112 p[r]=x;
113 }
114 void popf()
115 {
116 p[l]=0;
117 l=pos(l+1);
118 tot--;
119 }
120 void popb()
121 {
122 p[r]=0;
123 r=pos(r-1);
124 tot--;
125 }
126 }q;
127
128 int main()
129 {
130 q.init();//初始化有dp[0](l=r=1而不是l=1,r=0,tot=0),因为要用到
131 sc("%d%d",&n,&L);
132 for(int i=1;i<=n;++i)sc("%d",&a[i]),sum[i]=a[i]+sum[i-1];
133 for(int i=1;i<=n;++i)
134 {
135 while(q.l<q.r&&slope(q.f(),q.p[q.pos(q.l+1)])<2.0*A(i))q.popf();
136 dp[i]=dp[q.f()]+(A(i)-B(q.f()))*(A(i)-B(q.f()));
137 while(q.l<q.r&&slope(q.p[q.pos(q.r-1)],q.b())>slope(q.p[q.pos(q.r-1)],i))q.popb();
138 q.pb(i);
139 }
140 pr("%lld\n",(ll)dp[n]);
141 return 0;
142 }
143
144 /**************************************************************************************/
